A ship GMAW weld forming prediction method based on particle filtering

Abstract

The application provides a ship GMAW weld forming prediction method based on particle filtering, first selects a random process modeling mechanism to build a welding process and a molten pool characteristic uncertain noise (Hammerstein) model, and provides an accurate state space equation; secondly, Bayesian filtering is used for tracking training, particle filtering state estimation is realized through recursive prediction and observation correction; thirdly, the correction and system trajectory obtained by using clustering similarity measurement SIS and GPF are used to guide the generation of a new proposal distribution to improve particle degradation, and Monte Carlo sampling is updated to compensate for the importance weight, and resampling is replaced to eliminate particle depletion, so as to establish an improved particle filtering state tracking training and weld forming prediction model; finally, it is obtained through experiments that the state tracking training effect and the weld forming prediction accuracy of the particle filtering and the improved method can meet the requirements of the ship welding process, and the improved method has the advantages of better state tracking effect, higher forming prediction accuracy, stronger algorithm robustness and faster time efficiency.

Description

Technical Field

[0001] This invention relates to the fields of nonlinear filtering and intelligent ship manufacturing technology, specifically to a method for predicting the formation of GMAW weld seams in ships based on particle filtering. Background Technology

[0002] Gas metal arc welding (GMAW) using intelligent robots is receiving increasing attention as a crucial component of modern shipbuilding technology. Traditional shipbuilding GMAW welding processes rely primarily on manual experience and manual labor, resulting in high labor intensity for welders, low production efficiency, and difficulty in guaranteeing product quality. This necessitates a shift in shipbuilding GMAW welding from manual operations towards automation, robotics, and intelligentization. A prerequisite for achieving intelligent shipbuilding GMAW welding technology is the ability to describe various welding states—that is, to model the dynamic welding process. The aim is to elevate the understanding of welding phenomena to their essence, identifying the patterns and characteristics that characterize various welding behaviors, thus transforming technology into science and providing theoretical and technical support for welding automation and intelligentization.

[0003] Knowledge modeling in marine GMAW welding describes the specific functional relationships between various physical quantities, such as process parameter inputs and weld formation characteristics. It is generally expressed in physical or mathematical theoretical forms and represents a refinement and generalization of the welding process's essence. The accuracy of the model heavily depends on the understanding of the dynamic processes and patterns in marine GMAW welding. For predicting unmeasurable characteristics during welding, it is typically necessary to establish a mapping relationship between welding specification parameters and weld formation characteristics—that is, knowledge modeling of the welding dynamic process. Current research on welding process modeling mainly includes three categories: numerical simulation analysis, molten pool vibration methods, and artificial intelligence modeling. Numerical simulation analysis methods, based on certain theoretical assumptions, calculate the physical characteristics and laws of the thermal and flow fields of the molten pool and its surrounding environment during the welding process, and then establish the correspondence between these fields and welding parameters, such as temperature field models, weld depth and molten pool surface profile models, and plasma arc models. Qian Longgen et al. (application number 202210819398.6) proposed a numerical prediction method for laser weld morphology using classical physical functions of weld morphology, effectively solving the problem of over-reliance on data and scenarios in existing forming prediction methods; Qian Longgen et al. (application number 202210508734.5) proposed a pressure-based numerical calculation method for compressible two-phase flow to achieve high-precision prediction of weld morphology at the kilowatt level; Qian Longgen et al. (application number 202010723703.2) proposed using fast Fourier transform to solve welding heat transfer and flow equations, updating forming characteristic functions to improve prediction efficiency; Dong Zhongli et al. (application number 201310217892.6) used ANSYS to establish finite element analysis software to calculate forming dimensions based on the collection of welding process and material thermophysical parameters. It is concluded that although numerical simulation analysis methods have high prediction accuracy under theoretical assumptions, they are poor at describing complex and variable welding dynamic processes, have a large computational load, and are time-consuming, and are currently only applied to offline processes. The molten pool vibration method assumes that the molten pool can be represented by a mathematical model with certain parameters but a determined empirical structure. A deterministic relationship exists between the inherent oscillation frequency of the molten pool and the model parameters. By measuring the oscillation frequency of the molten pool, the unknown parameters of the molten pool model can be determined. Huang Jiankang et al. (application number 201621222464.8) constructed a pulsed laser-excited molten pool monitoring device to obtain the oscillation frequency of the TIG molten pool, calculated the molten pool quality forming result based on a dot matrix laser program, and called the corresponding welding parameters to achieve real-time control of weld penetration. This method can guarantee a high level of forming prediction accuracy under specific welding conditions, but it requires a large number of complex and specific measuring sensors, thus having certain application limitations.

[0004] Artificial intelligence modeling methods are crucial for achieving the required molten pool geometry, which is a prerequisite for weld quality. However, in practical engineering applications, the complex and diverse ship structures and processes limit the welding environment, making direct real-time online observation of molten pool geometry characteristics, such as weld width, reinforcement height, and penetration depth, difficult. Furthermore, extensive engineering practice and welder experience demonstrate a correlation between molten pool geometry and welding process parameters. By establishing this correlation through artificial intelligence, the prediction and control of molten pool geometry can be achieved. This invention primarily studies a knowledge modeling method for intelligent GMAW welding in ships, which falls under the category of artificial intelligence. With the continuous development of intelligent technologies, such as neural networks, support vector machines, fuzzy sets, and rough sets, more and more scholars are introducing artificial intelligence modeling methods into the prediction and control of dynamic welding processes. The dynamic process of GMAW welding in ships is characterized by strong nonlinearity, continuous time delay, multivariate coupling, uncertainties, and random disturbances. Artificial intelligence methods can, to a certain extent, provide a comprehensive and accurate description of the entire welding process.Chen Xi et al. (application number 202210579412.X) established a gray prediction model for weld measurement using ultrasonic testing technology, obtained the ultrasonic imaging width sequence of the test piece, and thus realized weld quality detection; John Paul Kulpewski et al. (application number 202210365023.7) used artificial intelligence algorithms to analyze and predict multiple sets of welding parameters, and obtained weld quality analysis by comparing the output results with the set judgment threshold; Lei Zhenglong et al. (application numbers 202111389993.2, 202111390016.4) disclosed two methods for predicting laser welding forming characteristics: a BP neural network method based on principal component analysis and genetic algorithm dual optimization, and a complementary dual-channel convolutional neural network; Zhang Yi et al. (application number 202110942162.7) established a quantitative regression model for weld pool images to realize the forming height prediction process; Tao Yong et al. (application number 202110754330.X) proposed a method based on intuitionistic fuzzy C-means clustering and adaptive inertia Weighted particle swarm optimization algorithm is integrated with an improved adaptive fuzzy neural network and applied to weld formation prediction; Yan Chunyan et al. (applications No. 202010927190.7, 202010781754.0) built an underwater wet welding platform to obtain samples, and established two methods for forming regression prediction based on gray relational analysis and second-order surface model based on welding parameter samples; Wang Jinzhao et al. (application No. 201911358046.X) designed corresponding process experiments to obtain a forming database, and established a weld formation prediction model based on deep neural network; Li Shichun et al. (application No. 201910939788.5) obtained multiple sets of welding process parameters by designing orthogonal experiments and established a multivariate nonlinear forming quality regression model; Huang Yongxian et al. (application No. 201910238706.4) calculated the flow field and temperature field distribution in the friction stir welding process, thereby obtaining the forming quality and defect distribution under different parameters, and used a generative adversarial network deep learning model to predict the forming results.

[0005] While artificial intelligence methods have made some progress in welding dynamic modeling, their implementation requires discretization of the continuous welding dynamic process and the incorporation of subjective factors and input parameters, which can affect the accuracy and timeliness of the results. Furthermore, the mathematical models established by these methods are based on deterministic system theory, where the relationship between input and output is strictly corresponding, and the influence of other disturbances in the process or system is generally not considered when obtaining the output from the model. However, ship GMAW welding processes are subject to various random and uncertain disturbances, such as unstable welding power output, weld gap variations, uncertain ambient temperature, thermal deformation, and heat accumulation. These factors introduce uncertainty into the welding system during operation, meaning the state of the weld pool will change under the influence of random factors. Therefore, this invention uses a stochastic theory model to describe the ship welding dynamic system, which is more consistent with the actual process. Particle filtering is used to establish a dynamic knowledge model of the ship GMAW process under the combined influence of system input and random disturbances. This fully leverages the algorithmic advantage of particle filtering, which requires less model input while still ensuring the accuracy of the output response, and also significantly reduces the hardware requirements for welding platform sensors and the computational cost of the model.

[0006] Particle filtering is a Bayesian state estimation algorithm based on Monte Carlo simulation, capable of handling any form of nonlinear non-Gaussian problem. It approximates the probability density function of a set of random samples propagating in the state space by replacing the integral operation with the sample mean, thus obtaining the minimum variance distribution of the state. However, during the sequential importance sampling process, the particle filtering algorithm assumes a known proposal distribution for the prior probability density, causing the particle weight variance to accumulate with the number of iterations. The weights of most particles decrease to a negligible level, a phenomenon known as particle degeneration. Degeneration means that continuous iteration consumes a large amount of computational resources on those insignificantly small-weight particles, resulting in excessive computation time waste and preventing the state estimate from accurately representing the true posterior distribution. To address particle degeneration, a resampling strategy is introduced to increase particle diversity, but this introduces a new problem: particles with larger weights are sampled multiple times, while particles with smaller weights are discarded. This results in many duplicate points in the sampling results, failing to effectively reflect the probability density distribution of the state variables, leading to sample impoverishment. Ultimately, this results in increased state estimation variance and significantly reduced filtering performance. Current solutions mainly focus on two aspects: the reasonable selection of the proposed distribution and the improvement of the resampling strategy.

[0007] Regarding the reasonable selection of the proposed distribution, Xu Bo et al. (application number 202011072157.7) used multi-rate consistent fusion technology to obtain the degree of influence of local observation nodes on global state variables; Xia Wei et al. (application number 202010042906.5) defined the cost function by introducing the Kullback-Leibler (KL) divergence between the true posterior distribution of the target state and the posterior distribution of particles; Li Liangqun et al. (application number 201910650468.8) introduced TS K-fuzzy models are used to model the dynamic system of the target; Zhou Zhaihe et al. (application number 201910291650.9) used a new quaternion distribution as the standard distribution of quaternions on the unit hypersphere; Liu Yu et al. (application number 201410783563.2) introduced network reliability and performed local reliability interaction and fusion through consistency iteration; Wang Hongjian et al. (application number 201310296086.2) selected fading factors and weakening factors to optimize the design of STSRCKF; Xia Yuanqing et al. (application number 201... 310645786.8) Obtains the measured value at time k and calculates its mean and variance through N parallel filtering processes; Zhu Zhiyu et al. (application number 201110308010.8) use the artificial fish swarm algorithm to guide prior particles to move towards the high likelihood region; Yang Meng et al. (application number 201010121599.6) adopt the SSUKF algorithm based on hyperspherical single-row sampling SSUT transform; Yang Meng et al. (application number 201010121571.2) use the particle swarm algorithm to optimize the estimation of the posterior probability of state tendency. In regions with high probability density, Ji Hongbing et al. (application number 200810232762.9) transformed a skipping quasi-Monte Carlo random sample sequence into a quasi-Gaussian sample sequence that follows a specified distribution; Zhao Qingjie et al. (application number 200710099440.7) used divide-and-conquer sampling strategies such as prior probability distribution, extended Kalman filter, and unscented Kalman filter to process sample particles; all of the above methods can achieve the purpose of optimizing or updating the proposed distribution, thereby improving the particle degradation phenomenon.

[0008] Regarding improvements to resampling strategies, Liu Haitao et al. (application number 202110195743.9) used an adaptive mutation strategy to cross-process preset weight thresholds; Lu Zhan et al. (application number 201611165889.4) used the variational Bayesian method to iteratively determine the distribution of unknown parameters in a Gaussian mixture model; Huang Zhenjin et al. (application number 201810980396.9) used a classification evolution method to generate new populations through fission, mutation, crossover, and selection of particle populations; Pan Jiahui et al. (Application No. 201510531989.3) borrows the idea of ​​guided filtering to retain some weight information of particles; Wang Jun et al. (Application No. 201410241879.9) uses a maximum likelihood sampling acceptance probability model based on GPU architecture; He Kang et al. (Application No. 201410052491.4) outputs replacement particles with small weights through comparison and exchange of FIFOs; Yu Xuelian et al. (Application No. 201510493464.5) sets a reasonable weight threshold and records random numbers falling within the threshold. The number of particles is used as the number of subsequent particle replicas; Zhou Yun et al. (application number 201510494727.4) designed an adaptive optimization method for importance weights; Wei Guohua et al. (application number 201410397456.6) grouped the importance weights into particles and calculated and compared the effective number of particles for linear processing; Li Hongwei (application number 201310695501.1) performed differential iterative optimization on the sampled particles to obtain the optimal particle set; Cong Li et al. (application number 201010121623.6) set... Parallel genetic resampling methods were used to establish information exchange models; Qin Honglei et al. (application number 200910238800.6) calculated the fitness of offspring individuals and sorted them in descending order, using niche-restricted competitive selection to make particles move towards higher fitness; Peng Xiyuan et al. (application number 201810136919.8) used the similarity between particle observation vectors and system states to adjust particle weights; all of the above methods can improve or modify the resampling process, thereby solving the particle poverty problem.

[0009] The analysis of the above research indicates that improvements to particle filtering primarily focus on particle degeneration and depletion. Solutions to these problems often rely on iterative optimization algorithms such as swarm optimization, bionics, and genetic mutation. However, these algorithms are complex to program, time-consuming, and prone to getting trapped in local optima or even iterative divergence. This severely impacts the timeliness and computational accuracy of state estimation using particle filtering methods, thus hindering their application. The increasing complexity of GMAW welding in modern shipbuilding, characterized by higher levels of system nonlinearity, coupled with the complex characteristics of the likelihood function observed in the welding process, makes the state estimation problem even more difficult. While the aforementioned conventional improved filtering methods alleviate particle degeneration and depletion to some extent, they still suffer from low estimation accuracy and poor stability, failing to meet the demands of modern engineering. Therefore, based on the beneficial results achieved by applying the particle filtering method to the prediction of GMAW quality in ships, this invention proves the feasibility of particle filtering in the dynamic modeling of GMAW welding in ships. At the same time, considering the shortcomings of the particle filtering algorithm itself, a clustering similarity particle filtering algorithm based on spatial state trajectory consistency is proposed for the welding formation prediction method. The proposed method is completely different from the above-mentioned iterative optimization improvement ideas such as crowd intelligence and bionics. It adopts the principle of state trajectory consistency and the data mining idea - clustering analysis method to measure the similarity of current and future multi-stage measurement information to improve the proposed distribution, guide the importance sampling process to effectively improve the particle degradation problem, and abandon the resampling strategy to fundamentally solve the particle depletion problem. Summary of the Invention

[0010] To address the technical problems mentioned in the background section, this invention proposes a particle filtering method to solve the knowledge modeling problem of GMAW welding process for ship hull structures under random noise interference and strong nonlinear system characteristics. The model obtained by this method will be more consistent with the actual process when used to describe the dynamic system of ship welding, thereby improving the accuracy of GMAW weld formation prediction.

[0011] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0012] A particle filter-based method for predicting the formation of GMAW weld seams in marine applications includes the following steps:

[0013] S1, Construction and test design of the experimental platform for the GMAW welding system of the hull structure: The experimental platform for the GMAW welding system of the hull structure is constructed. Welding orthogonal tests are designed to obtain welding process parameters that meet the forming specifications. Then, corresponding test schemes for weld tracking and real-time acquisition of molten pool are formulated.

[0014] S2, Real-time acquisition and preprocessing of welding information during welding formation: During the weld tracking and real-time acquisition of the molten pool test, image information is acquired in real time based on the molten pool image sensor and the geometric features of the image are extracted to obtain the weld size online in real time. The welding current and arc voltage are acquired through the Hall sensor, and the wire filling rate is acquired through the welding machine. The acquired welding information is preprocessed, including welding current, arc voltage and wire filling rate.

[0015] S3, the architecture of the state-space equation for particle filter welding forming prediction, includes the following steps:

[0016] S31, Analyze and determine the type of interference noise;

[0017] S32, Based on the determined type of interference noise, establish a nondeterministic noise Hammerstein stochastic system model for the dynamic process of ship GMAW welding;

[0018] S33, perform structural parameter identification analysis on the nondeterministic noise Hammerstein stochastic system model of the ship's GMAW welding dynamic process;

[0019] S34. Design a welding process step response test to obtain the transfer function and corresponding parameters of the weld pool shape under positive / negative step conditions of welding current and wire filler rate, so as to provide a basis for model structure optimization and identification.

[0020] S35, using the least squares identification method and the final prediction error criterion, the model structure of the nondeterministic noise Hammerstein stochastic system model of the ship GMAW welding dynamic process is optimized and identified, thereby constructing the state space equation for particle filter welding forming prediction.

[0021] S4, Bayesian welding state tracking training: The welding information after preprocessing in step S2 is divided into training set and test set to provide data support for Bayesian welding state tracking training and welding formation prediction. The Bayesian filter trained by state tracking is used to optimize the parameters of the state space equation of the welding formation prediction, and then a dynamic forming prediction model of ship structure welding based on particle filter is constructed.

[0022] S5, Nonlinearization of welding dynamic system, initialization of sampling particles and corresponding weights: The nonlinear welding process is defined by using a particle filter-based prediction model for the dynamic forming of hull structure welding. Monte Carlo sampling of the welding forming state is realized by recursive prediction of forming and observation correction and update. Since the posterior probability density function is unknown, the importance probability density function is selected to satisfy the Monte Carlo sampling, thereby approximating the particle set.

[0023] S6, Sequential Importance Sampling: Assuming the prior probability distribution is used as the importance probability density function, that is, the proposal distribution guides the particles to perform sequential importance sampling, and then recursively calculates the importance weight of the sampled particles.

[0024] S7, Clustering similarity measurement of welding forming state trajectory similarity: Through state space joint trajectory feature mining and vector planning, clustering analysis method is used to measure the similarity of measurement information of current stage sequential importance sampling and future multi-stage Gaussian filter prediction.

[0025] S8, Correcting the importance probability density function: Using the similarity metric from step S7 to guide the generation of a new proposal distribution, thereby updating the importance probability density function in step S6 to compensate for the correction of the Monte Carlo sampling process;

[0026] S9, Update Markov Importance Weights: Update the importance weights of the first-order Markov model in step S6 using the proposed distribution corrected in step S8, and normalize the particle weights to obtain the prediction results of the welding forming state at the current moment.

[0027] S10, steps S5-S9 constitute an iterative process for predicting and estimating the welding forming state using a particle filtering method based on state trajectory clustering similarity; repeat steps S6-S9 to sequentially output the prediction results of ship GMAW weld forming using clustering similarity particle filtering.

[0028] Furthermore, in step S31, the interference noise affects the prediction model of the dynamic forming of the hull structure welding in two ways: deterministic interference and random interference noise. Deterministic measurement information... It can be represented as:

[0029]

[0030] In the formula, T and ψ represent the measured value, the true value, and the deterministic interference noise of the system, respectively.

[0031] Random measurement information It can be represented as:

[0032]

[0033] In the formula, random measurement information It is a nonadditivity function of T(t) and Ψ(t), where Ψ(t) is random interference noise and t refers to the acquisition time.

[0034] Furthermore, the time-domain expression of the nondeterministic noisy Hammerstein stochastic system model described in step S32 is:

[0035]

[0036] Wherein, Γ(k) is a 1×[l+p×(m+1)] dimensional vector;

[0037] θ is a [l+p×(m+1)]×1 dimensional vector;

[0038] l and m are the orders of the linear subsystem;

[0039] p is the highest power of the nonlinear element;

[0040] e(k) is the equivalent synthesized noise, and k is the time step;

[0041] Γ and θ represent the model structure and parameters, respectively.

[0042] Further, step S33 includes the following steps:

[0043] First, the pure delay coefficient is determined using the step response identification method; second, assuming the order of the linear subsystem, the highest power of the nonlinear element is obtained using the recursive least squares method; finally, the optimal selection and evaluation of the order of the linear subsystem is performed using the final prediction error criterion.

[0044] Further, in step S35, the step of optimizing and identifying the model structure of the stochastic model of the ship GMAW welding dynamic process using the least squares identification method and the final prediction error criterion includes: after determining the pure delay coefficient of the welding process parameters, first assuming that the order of the linear subsystem is known, and taking k = k0 + 1, ..., k0 + N (N ≥ l + p × (m + 1)) for the time-domain expression of the nondeterministic noise Hammerstein stochastic system model, the least squares normal equation is obtained:

[0045]

[0046] Error criterion function:

[0047]

[0048] Taking the minimum value of the error criterion function, the least squares solution is obtained as follows:

[0049]

[0050] Model parameter correspondence

[0051]

[0052] The above algorithm slows down as the amount of data increases, and too much old information weakens the effect of new information. Considering the real-time nature of the model structure, a recursive least squares identification method is adopted. The least squares normal equation for N sets of observation data is assumed to be: When the N+1th set of data is measured At that time,

[0053]

[0054] assumed The recursive formula is:

[0055]

[0056]

[0057] The above formula can be simplified to

[0058]

[0059] The initial value for recursion can be selected as follows:

[0060]

[0061] The final error criterion of the recursive algorithm:

[0062]

[0063] Where ε = 10 -5 .

[0064] Furthermore, in step S35, the weld pool feature size - front weld width W is used. f As system outputs, the system inputs consist of welding process parameters – welding current I and wire filler ratio V. f To represent; and the mathematical expression of the state-space equation for the predicted welding forming is:

[0065]

[0066] In the formula, Represents the output width W f ;

[0067] and These represent the input welding current and the wire fill rate, respectively.

[0068] e(k) is the equivalent composite noise;

[0069] l represents the order of the historical moment of the output parameter melt width in the linear subsystem;

[0070] m1 and m2 are the orders of welding current and wire fill rate in the linear subsystem, respectively;

[0071] p1 and p2 are the highest powers of the welding current and wire fill rate in the nonlinear link, respectively.

[0072] d1 and d2 are the pure delay coefficients of welding current and wire fill rate in the nonlinear link, respectively.

[0073] and These are the structural coefficients for welding current and wire fill rate in the nonlinear process, respectively.

[0074] α i The order factor representing a historical moment in the melting point width;

[0075] and These represent the order coefficients of the welding current and the wire fill rate in the linear subsystem, respectively.

[0076] Furthermore, the method for dividing the preprocessed welding information from step S2 into a training set and a test set in step S4 is as follows:

[0077] Using the welding information preprocessed in step S2 as the original dataset, a Bayesian tracking training model is established to determine the parameters of the state equation: the first S sets of data from the preprocessed original historical dataset AX are used as the training set AT for state tracking training, i.e., AT = AX(1:S, :) = [ATI, ATV, ..., ATB, ATD, ...], where ATI, ATV, ATB, and ATD represent the tracking sets of welding current, wire fill rate, and corresponding weld width and penetration depth, respectively; the data TX after the S sets of the preprocessed original dataset AX are used as the test set for comparison between the true and predicted values, i.e., TX = OX(:, S+1:N) = [TXI, TXV, ..., TXB, TXD, ...]; Bayesian theory is used to train the state tracking model on the test set AT, and the optimal model parameters that minimize the error between the algorithm's predicted values ​​and the experimental true values ​​are estimated using minimum variance unbiased estimation, thereby improving the state space equation for welding formation prediction.

[0078] Further, step S7 includes:

[0079] S71, Feature Mining and Vector Programming of Joint State-Space Trajectory (Normal and Corrected Trajectories):

[0080] The set of particles representing the joint trajectory of the welding forming state from time k to k+L+l is selected as... in Follows the SIS filtering process, x′ j(i) It follows the GPF prediction process, where L is the length of the filtered trajectory and l is the length of the predicted trajectory. Since the actual welding forming state of the system is unknown, the consistency of the forming state trajectory is characterized by the process observation likelihood function. The corresponding likelihood trajectory is solved by the process observation equation based on the forming state trajectory of the sampled particles. in

[0081]

[0082] S72, Similarity Measurement of Actual Welding Formation State and Particle Process Observation Likelihood Trajectory: The method for measuring the similarity between the measurement information predicted by the current stage filtering and the future multi-stage Gaussian filtering using cluster analysis is as follows: The process observation likelihood trajectory corresponding to the actual welding system formation state is {Z}. k}={z j :j=k,…,k+L+l}, spatial trajectory clustering consistency analysis is used, and distance similarity metric is selected to measure the distance similarity between the actual welding forming state and the particle process observed likelihood trajectory. The calculation is as follows:

[0083]

[0084] Where dis(*) represents the distance similarity function, and dis(*)≥0, ξ is the metric type parameter;

[0085] To enhance the reliability of the algorithm's output, an exponential function structure is used to perform an exponential transformation on the above equation to obtain the updated similarity metric D. k (i)

[0086]

[0087] Where λ is the reliable gradient factor.

[0088] Further, step S8 includes: based on the distance similarity measure between the process observation likelihood trajectory and the measured likelihood trajectory of the sampled particles obtained in step S72, applying the similarity correction formula to the prior probability distribution p(x) according to the following formula. k |x k-1 The importance of substitution probability density function π(x) k |x 0：k-1 , z 1：k ):

[0089] π(x k |x 0：k-1 , z 1：k ) = D k *p(x k |x k-1 ).

[0090] This invention also provides another particle filter-based method for predicting the formation of GMAW weld seams in marine applications, comprising the following steps:

[0091] S1, Construction and test design of the experimental platform for the GMAW welding system of the hull structure: The experimental platform for the GMAW welding system of the hull structure is constructed. The welding orthogonal test is optimized to obtain the welding process parameters that meet the forming specifications. Then, the corresponding test plan for weld tracking and real-time acquisition of molten pool is formulated.

[0092] S2, Real-time acquisition and preprocessing of welding information during welding formation: During the weld tracking and real-time acquisition of the molten pool test, image information is acquired in real time based on the molten pool image sensor and the geometric features of the image are extracted to obtain the weld size online in real time. The welding current and arc voltage are acquired through the Hall sensor, and the wire filling rate is acquired through the welding machine. The acquired welding information is preprocessed, including welding current, arc voltage and wire filling rate.

[0093] S3, the architecture of the state-space equation for particle filter welding forming prediction, includes the following steps:

[0094] S31, Analyze and determine the type of interference noise;

[0095] S32, Based on the determined type of interference noise, establish a nondeterministic noise Hammerstein stochastic system model for the dynamic process of ship GMAW welding;

[0096] S33, perform structural parameter identification analysis on the nondeterministic noise Hammerstein stochastic system model of the ship's GMAW welding dynamic process;

[0097] S34. Design a welding process step response test to obtain the transfer function and corresponding parameters of the weld pool shape under positive / negative step conditions of welding current and wire filler rate, so as to provide a basis for model structure optimization and identification.

[0098] S35, using the least squares identification method and the final prediction error criterion, the model structure of the nondeterministic noise Hammerstein stochastic system model of the ship GMAW welding dynamic process is optimized and identified, thereby constructing the state space equation for particle filter welding forming prediction.

[0099] S4, Bayesian welding state tracking training: The welding information after preprocessing in step S2 is divided into training set and test set to provide data support for Bayesian welding state tracking training and welding formation prediction. The Bayesian filter trained by state tracking is used to optimize the parameters of the state space equation of the welding formation prediction, and then a dynamic forming prediction model of ship structure welding based on particle filter is constructed.

[0100] S5, Nonlinearization of welding dynamic system, initialization of sampling particles and corresponding weights: The nonlinear welding process is defined by using a particle filter-based prediction model for the dynamic forming of hull structure welding. Monte Carlo sampling of the welding forming state is realized by recursive prediction of forming and observation correction and update. Since the posterior probability density function is unknown, the importance probability density function is selected to satisfy the Monte Carlo sampling, thereby approximating the particle set.

[0101] S6, Sequential Importance Sampling: Assuming the prior probability distribution is used as the importance probability density function, that is, the proposal distribution guides the particles to perform sequential importance sampling, and then recursively calculates the importance weight of the sampled particles.

[0102] S7, Resampling Strategy: Measure the degree of weight degradation and determine whether resampling is needed. If so, resample the particles according to the particle weight iteration value and normalize the particle weight to obtain the prediction result of the ship GMAW weld formation at the current moment.

[0103] S8, steps S5-S7 constitute one iteration of the state estimation process of the traditional particle filter method; repeat steps S6-S7 to output the prediction results of the ship GMAW weld formation at different times in sequence.

[0104] By adopting the above technical solution, the present invention has the following beneficial effects:

[0105] (1) Stochastic theoretical framework of ship GMAW process noise

[0106] The GMAW welding process in marine applications is subject to various random and uncertain disturbances, such as unstable welding power supply output, weld gap variations, uncertain ambient temperature, thermal deformation, and heat accumulation. These factors introduce uncertainty into the welding system's operation, meaning the state of the weld pool will change under the influence of random factors. Currently, most artificial intelligence modeling methods are based on deterministic system theory, where the relationship between input and output is strictly corresponding. The process of obtaining the output from the model generally does not consider the influence of time-varying processes or other disturbances within the system. Therefore, this invention employs a stochastic theoretical model to describe the dynamic system of ship welding, which is more consistent with the actual process. Addressing the knowledge modeling problems related to the nonlinearity, time delay, multivariate coupling, uncertainties, and random disturbances in ship GMAW welding, this invention introduces a stochastic process mechanism to establish a nondeterministic, nonlinear Hammerstein noise model between welding specification parameters and weld pool shape parameters. This model accurately reflects the characteristics and effects of random noise in the actual welding process. Based on online constant specification step response tests and identification techniques such as recursive least squares and final prediction error criteria, the noise model structure is identified and optimized to obtain the state-space equation characterizing the welding formation mechanism. The model obtained by this method will better conform to the welding formation law when describing the dynamic system of ship welding. This provides theoretical support and accuracy assurance for knowledge modeling of the particle filter welding dynamic process, thereby improving the accuracy of ship GMAW weld formation prediction.

[0107] (2) Knowledge Modeling for Weld Formation Prediction Using Particle Filtering

[0108] Particle filtering has unique advantages in handling state estimation problems of non-Gaussian, nonlinear time-varying systems and random noise interference. This invention is the first to apply this method to knowledge modeling of the GMAW welding process in ships. Particle filtering is used to establish a dynamic knowledge model of the GMAW process in ships under the combined effects of nonlinear system process input and random noise interference. This method abandons previous modeling methods that relied heavily on prior knowledge, expert experience, and hardware testing techniques, incorporating a large number of subjective factors and input technical parameters. It fully leverages the advantages of particle filtering to deeply mine and reveal the temporal changes of welding process laws and weld formation mechanisms, i.e., the time dynamic relationship between welding process parameters and molten pool geometry. It also maintains the accuracy of output response results with fewer model inputs, significantly reducing the requirements for welding platform sensor hardware and model computation and operation costs. Simulation results show that the state tracking training effect is good, ensuring accurate extraction of the characteristic parameters related to the formation mechanism implicit in the tracking set; the predicted weld formation trend is consistent with the actual change curve of the test set, and the accuracy is maintained within 0.88mm. Therefore, the proposed method for predicting the weld formation of ship GMAW based on traditional particle filtering can meet the requirements of ship welding process in terms of state tracking training effect and weld formation prediction accuracy. This shows that the particle filtering method has certain applicability in the application of dynamic knowledge modeling in GMAW, and also provides a technical basis for monitoring the weld formation quality in the ship GMAW welding process.

[0109] (3) Application of particle filtering improvement method in welding process modeling

[0110] The particle filtering method based on state trajectory clustering similarity improves the particle filtering method itself without relying on external methods, and restructures the algorithm logic framework: Addressing the particle degeneration phenomenon caused by unknown and assumed prior probability distributions, the particle filtering algorithm serves as the core modeling framework and theoretical analysis basis. It utilizes SIS and GPF methods to obtain corrected trajectories combining current and future multi-stage spatial state information, and performs clustering analysis—distance similarity measurement—with the system's true state trajectory. Higher consistency similarity indicates a closer representation to the true state, guiding the generation of new proposed distributions to improve particle degeneration. Simultaneously, the first-order Markov process is updated to compensate for the revised importance weight calculation. By selectively integrating the updated compensation scheme (clustering metric) into the latest phased measurement information during the importance sampling process to replace the resampling process, the particle depletion problem can be fundamentally eliminated, and timeliness is significantly improved. Based on the convergence theorem proof of the improved algorithm CSPF (Clustering Similarity Particle Filtering), and through experimental verification, compared with the traditional PF (Particle Filtering) and APF (Auxiliary Particle Filter), CSPF has advantages such as better state tracking, higher forming prediction accuracy, stronger algorithm robustness, and faster timeliness in the application of knowledge modeling of GMAW process of ship structure.

[0111] Therefore, the present invention uses a stochastic theoretical model to describe the dynamic system of ship welding, which is more in line with the actual process. It uses particle filtering to establish a dynamic knowledge model of the ship GMAW process under the combined effect of system input and random disturbance factors. This fully leverages the inherent advantage of particle filtering algorithm, which can still guarantee the accuracy of output response results with less model input. At the same time, it also significantly reduces the requirements of welding platform sensor hardware and model calculation and operation costs. Attached Figure Description

[0112] Figure 1 A schematic diagram of the experimental platform for the GMAW welding system of the ship hull structure;

[0113] Figure 2 A Hammerstein stochastic system model for the nondeterministic noise of the GMAW welding process for the ship's hull structure;

[0114] Figure 3 The transient response of weld width to current step;

[0115] Figure 4 The transient response of weld width and wire filler ratio;

[0116] Figure 5 A schematic diagram of the process for spatial state structural identification of a nonlinear GMAW welding system for ship hull structures;

[0117] Figure 6 This is a schematic diagram of the traditional particle filter resampling strategy process;

[0118] Figure 7 This is a flowchart illustrating the state tracking and forming prediction method for the dynamic process of GMAW welding of ship hull structure according to the second embodiment of the present invention.

[0119] Figure 8 The figure shows the effect of tracking the dynamic process of ship welding based on four nonlinear prediction models.

[0120] Figure 9 This is a comparison chart of RMSE results based on four nonlinear models for shaping prediction. Detailed Implementation

[0121] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0122] It should be noted that when a component is described as "fixed to" another component, it can be directly on the other component or may have a component in between. When a component is considered "connected to" another component, it can be directly connected to the other component or may have a component in between. When a component is considered "set on" another component, it can be directly set on the other component or may have a component in between. The terms "vertical," "horizontal," "left," "right," and similar expressions used in this document are for illustrative purposes only.

[0123] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0124] A preferred embodiment of the present invention provides a method for predicting the formation of GMAW weld seams in marine applications based on particle filtering, comprising the following steps:

[0125] S1. Construction and test design of the experimental platform for the GMAW welding system of the hull structure: The experimental platform for the GMAW welding system of the hull structure is constructed. Welding orthogonal tests are designed to obtain welding process parameters that meet the forming specifications. Then, corresponding test schemes for weld tracking and real-time acquisition of molten pool are formulated.

[0126] In this embodiment, step S1 includes:

[0127] S11, Construction of the GMAW Welding System Experimental Platform for Ship Structure: This experimental platform for the GMAW welding system for ship structure mainly consists of a Kuka Arc5 robot, a pulsed GMAW power supply system, an industrial control computer (IPC), a data acquisition card, an intelligent wire feeder, a vision sensing system, Hall sensors, and a laser weld seam tracking system. Figure 1 As shown. The laser weld seam tracking system identifies the weld seam trajectory through laser scanning, guiding the Kuka Arc5 robot to autonomously move and adjust the welding torch posture for accurate and efficient welding preparation. Hall effect sensors can collect welding current and arc voltage in real time during the operation. The vision sensing system consists of a CCD camera lens and a composite reduction and filtering system. By adjusting the relative position of the CCD camera and the workpiece plate through a coupling fixture, it can acquire the forming geometry features of the front and back of the molten pool in real time. The intelligent wire feeder is an autonomously driven mechanized wire feeding device that delivers welding wire to the welding torch position according to instructions from the industrial control computer (IPC). The pulsed GMAW power supply system provides a continuous and stable welding current and arc voltage for arc welding, communicates with the robot system, and receives its instructions. The regulator performs noise reduction preprocessing on the acquired molten pool image information. The data acquisition card (DAQ) has a sampling frequency set to 40kHz, which quantizes the acquired analog signals into digital signals and sends them to the IPC's data analysis module. The processed welding process parameters (welding current, wire filler ratio, etc.) and weld formation geometric features (weld width, reinforcement height, etc.) are input into the knowledge modeling module of the industrial control computer to predict the posterior probability estimate of the formed weld, thereby providing technical support for future research on welding quality monitoring and control. The structure of this ship hull structure GMAW welding system experimental platform is existing technology and will not be described in detail here for brevity.

[0128] S12, Optimize the design of orthogonal welding experiments to obtain the optimal welding forming process parameters. Extensive engineering practice and welder experience show a correlation between molten pool geometry and welding process parameters. Adjusting these parameters allows for the prediction and control of molten pool geometry. Under reasonable welding process parameters, the random variation ranges of welding current and wire filler ratio were selected and determined. Based on this, orthogonal experiments were designed for robotic GMAW welding to obtain welding process parameters that meet the forming requirements and extract the molten pool shape parameters under the corresponding conditions. Specific welding process conditions are shown in Table 1.

[0129] Table 1. GMAW Random Test Conditions for Hull Structure

[0130]

[0131] S2, Real-time acquisition and preprocessing of welding information during welding formation: During the weld tracking and real-time acquisition of the molten pool test, image information is acquired in real time based on the molten pool image sensor and the geometric features of the image are extracted to obtain the weld size online in real time. The welding current and arc voltage are acquired through the Hall sensor, and the wire filling rate is acquired through the welding machine. The acquired welding information is preprocessed, including welding current, arc voltage and wire filling rate.

[0132] Various uncertainties exist during GMAW welding in marine applications. These interfering factors are all random in nature, such as unstable outputs of process parameters like welding current, wire filler, shielding gas flow rate, and pulsed power supply, as well as variations in weld gap, uncertainties in ambient temperature, thermal deformation, and heat accumulation. These factors introduce a degree of uncertainty into the welding system's operation, meaning the state of the weld pool will change under the influence of random factors. Therefore, uncontrollable random noise interference during experimental data acquisition can lead to abnormal data in weld formation information. Furthermore, excessive data volume increases computational load and reduces timeliness; hence, preprocessing steps such as screening and simplification are necessary.

[0133] S3, the architecture of the state-space equation for particle filter welding forming prediction, includes the following steps:

[0134] S31, Analyze and determine the type of interference noise.

[0135] For the GMAW welding process of ship hull structures, if various process conditions are ideal, such as standardized plate shapes, constant weld gaps, stable gas flow and heat dissipation, constant ambient temperature, and no noise interference, then using constant standard welding parameters can achieve a stable welding process, thereby ensuring the stability of weld formation and welding quality. However, in actual welding environments, the above working conditions (including welding process parameters) are unstable and their changes are unpredictable. This randomness of working conditions inevitably affects the stability of the welding process, making the welding results also random. Furthermore, during the system parameter identification and knowledge modeling process, some process parameter data are collected by measuring instruments during the dynamic welding process, and the measured values ​​are subject to errors due to noise interference. The effects of interference noise on the prediction model of the dynamic forming of ship hull structure welding can be divided into two categories: deterministic interference and random interference noise. Deterministic measurement information... It can be represented as:

[0136]

[0137] In the formula, T and ψ represent the measured value, the true value, and the deterministic interference noise of the system, respectively.

[0138] Random measurement information It can be represented as:

[0139]

[0140] In the formula, random measurement information It is a non-additive function of T(t) and Ψ(t), where Ψ(t) is random noise, and t represents the acquisition time. These disturbances cause certain process parameters in the welding dynamic system to become random variables. Only by introducing random processes into the welding dynamic model can the characteristics and effects of random noise in the actual welding process be truly reflected.

[0141] S32. Based on the determined type of interference noise, establish a nondeterministic noise Hammerstein stochastic system model for the dynamic process of ship GMAW welding.

[0142] GMAW welding is a heat treatment process in which the metal of a ship's hull structure undergoes heating, melting, solidification, and continuous cooling under the influence of an electric arc heat source, ultimately forming a weld. Based on the theory of arc welding heat sources and heat transfer processes, the welding process can be viewed as an excitation source of a dynamic system by an electric arc heat source. The arc process can be considered a static nonlinear function process, and the welding heat transfer process can be approximated by a dynamic linear system. For the dynamic system decomposed into nonlinear and linear subsystems, a special structural form, the Hammerstein model, is used for simulation and reproduction, as shown below. Figure 2 . Figure 2 In the middle, L q =q -d The time shift operator is the pure delay element; d is the output pure delay coefficient; γ(k) = γ1u + γ2u 2 +…+γ p u p +ψ(k) represents a memoryless nonlinear element; the linear dynamic element can be equivalent to:

[0143]

[0144] Where, u(k) and These represent the input and actual output variables of the system process, respectively; γ(u) and γ(k) are the input function and output variable of the nonlinear element, respectively. The equivalent synthesized noise is given by ψ(k), where ψ(k) is the deterministic interference noise of the nonlinear element, Ψ(k) is the random interference noise of the linear subsystem, and B(*) and A(*) are related to the output variables. Complex linear functions.

[0145] In actual welding processes, there are many sources of interference noise. During model construction, all random noise influences are integrated and replaced by an equivalent noise level. Figure 2 The model can be simplified to a time-domain expression:

[0146]

[0147] Further expansion yields:

[0148]

[0149] make

[0150]

[0151] θ = [α1, α2, ..., α l ,β0γ1,β1γ1,…,β m γ1, β0γ2, β1γ2,…,β m γ2,β0γ p ,β1γ p , ..., β m γ p ] T

[0152] Therefore, the time-domain expression of the nondeterministic noisy Hammerstein stochastic system model is obtained as follows:

[0153]

[0154] Wherein, Γ(k) is a 1×[l+p×(m+1)] dimensional vector;

[0155] θ is a [l+p×(m+1)]×1 dimensional vector;

[0156] l and m are the orders of the linear subsystem;

[0157] p is the highest power of the nonlinear element;

[0158] e(k) is the equivalent synthesized noise, and k is the time step;

[0159] Γ and θ represent the model structure and parameters, respectively.

[0160] S33, perform structural parameter identification analysis on the nondeterministic noise Hammerstein stochastic system model of the dynamic process of GMAW welding in the ship.

[0161] Model structure identification is the prerequisite and guarantee for welding formation prediction. In system identification, there are various methods for selecting structural parameter estimation, such as the Akaike criterion, rank estimation of the Hankel matrix, determinant ratio, variance estimation of residuals, recursive least squares method, and final prediction error criterion. This invention, under a reasonable design of the identification experiment, uses a combination of step response, least squares method, and final prediction error criterion to estimate the structural parameters of the Hammerstein random noise model. In this embodiment, step S33 includes: first, determining the pure delay coefficient using the step response identification method; second, assuming the order of the linear subsystem, obtaining the highest power of the nonlinear element using the recursive least squares method; and finally, evaluating the optimal selection of the order of the linear subsystem using the final prediction error criterion. In this embodiment, welding current and wire fill rate are selected as model input parameters, and the front weld width, representing the geometric characteristics of the weld pool, is used as the input parameter.

[0162] S34. Design a welding process step response test to obtain the transfer function parameters of the weld pool shape under positive and negative step conditions of welding current and wire fill rate, so as to provide a basis for model structure optimization and identification.

[0163] In this embodiment, a welding process step test is designed in step S34, and the step response is identified using the area method, thereby obtaining the transfer function and corresponding parameters of the weld pool shape under positive / negative step conditions of welding current and wire filling rate, providing a basis for the structural identification of the weld formation prediction model.

[0164] Step signals are simple and easy to obtain, and their response can reflect the main information of welding dynamic characteristics, thus they can also be used as input signals for system identification. Methods for determining the process transfer function using step response include approximation methods, semi-logarithmic methods, tangent methods, two-point methods, and area methods. This invention uses the relatively mature area method for step response identification, and the specific steps are as follows:

[0165] 1) Design a step response welding process experiment and obtain input and output data;

[0166] 2) Perform necessary preprocessing on the data, including simplification and filtering;

[0167] 3) Plot the model response curve and perform model validation;

[0168] 4) Transform the identified discrete model into a continuous transfer function expression;

[0169] 5) Determine the pure delay coefficient d of the model based on welding experience and transfer function.

[0170] In this embodiment, the material selected for the step response test is low-carbon steel Q235, the GMAW welding method is carbon dioxide gas shielded welding, which is most commonly used in shipbuilding, and the welding process is butt welding. The process parameters of the welding specification are determined through a rule database: the welding current I ranges from 120A to 170A, and the arc voltage is V. A =20V, welding speed is V W =2.5mm / s, with a plate gap of g=4.0mm. During the current step test, the arc voltage and welding speed were kept constant. The positive step of the welding current I was 50A, increasing from 120A to 170A, and the negative step value increased from 170A to 120A. During the welding process, after running at the initial current for 60 sampling points, a step change was generated by the current controller. The output result after the step response, starting from the 61st sampling point, was used to obtain the weld pool characteristic parameter – weld width W – using the weld pool image sensing system. f The transfer function under the negative current step condition can be obtained using the same identification method; please refer to [link to relevant documentation]. Figure 3 , Figure 3 The transient response of weld width and current step is given. Figure 3 Figure (a) shows a positive current step, Figure (b) shows a positive weld width step, Figure (c) shows a negative current step, and Figure (d) shows a negative weld width step.

[0171] Determining the pure delay coefficient of the welding process parameters requires knowledge of the transfer function of the step response. From Figure 3 The data distribution shows that there is no oscillating element in the welding process under the current step response. Therefore, the process can be considered a first-order system, and its transfer function is as follows:

[0172]

[0173] Where K is the step response gain coefficient, t is the time constant, d is the pure delay coefficient, and s is the spatial variable. Since the structural order of the system transfer function is determined, the parameters that determine the minimum condition of the fit and the final prediction error FPE are used as the pure delay coefficients, thereby determining the other characteristic parameters of the transfer function. The transfer function parameters for the molten pool shape characteristics of positive and negative current steps are shown in Table 2 below.

[0174] Table 2 Transfer function parameters for weld shape characteristics under current step response

[0175]

[0176] As can be seen from the identification results in Table 2, the weld width W under positive and negative step current conditions... f The time delay in the response is not significant, while the melt width W under the positive step condition is... f The time delay constant (i.e., the delay coefficient) d is larger with respect to the negative step, indicating that the weld formation of marine low-carbon steel is more sensitive to a decrease in heat input than to an increase of the same amount of heat input; the weld width W under the positive step condition f The gain coefficient K and time constant t are relatively large compared to the negative step, indicating that the weld formation is not only determined by the heat input but also by the arc thrust. As the current decreases, the arc thrust decreases rapidly, causing the weld formation characteristics to change rapidly. The parameters of the transfer function obtained in the positive and negative step stages of stable welding are different, indicating that the welding process has nonlinear, strong coupling, and variable time delay characteristics. Therefore, the knowledge modeling of the welding process should fully consider the above influencing factors.

[0177] In GMAW welding of ship hull structures, the wire filler ratio and the wire feed rate it determines are crucial to weld formation. Changes in the wire feed rate directly alter weld width, reinforcement height, and other weld geometric characteristics. Once the wire diameter, wire feed method, and welding oscillation are determined, only the wire filler ratio can determine the wire feed effect. Therefore, the wire filler ratio must be considered as an influencing factor in weld formation during the knowledge modeling of the welding process. This experiment selected a wire filler ratio V... F The current feed rate ranged from 2.6 to 4.5 m / min, with other welding process parameters referenced from the current step experiment. During welding, 60 sampling points were run at the initial wire fill rate. The wire feed rate was increased to 1.9 m / min using the wire feeder. The weld pool characteristic parameter – weld width W – was acquired using a weld pool image sensing system. f Using a similar identification method, the transfer function parameters of the weld pool shape under the negative step condition of the wire filler ratio can be obtained. The specific wire feeding step response is shown below. Figure 4 , Figure 4 The transient response to the step change in weld width and wire fill rate. Figure 4Figure (a) represents a positive step in wire filler ratio, Figure (b) represents a positive step in weld width, Figure (c) represents a negative step in wire filler ratio, and Figure (d) represents a negative step in weld width.

[0178] from Figure 4 The data distribution pattern shows that the step response of the wire filler ratio should have a similar functional structure to the welding current step. Using a similar identification method, the transfer function parameters of the weld pool shape under positive / negative step conditions of the wire filler ratio can be obtained, as shown in Table 3 below.

[0179] Table 3 Transfer function parameters of weld shape characteristics under the step response of welding wire filler ratio

[0180]

[0181] The parameter identification results in Table 3 show that the weld width W under both positive and negative step conditions of the wire filler ratio is... f The time-delay characteristic of the response is also not obvious. Under the positive step condition of the filler wire ratio, the time delay constant (i.e., the delay coefficient) d approaches 0 and is smaller than that under the negative step condition, while the time constant t is much larger than that under the negative step condition. This indicates that the increase in the amount of filler wire leads to a sharp increase in the arc thrust, which in turn rapidly affects the weld formation. Under the positive step condition of the filler wire ratio, the weld width W... f The gain coefficient K should be less than the weld width W under the negative step condition of the wire filler ratio. f The gain coefficient K indicates that increasing the wire feed rate requires more heat to melt the welding wire. This also shows that welding current and wire filler ratio play a decisive role in the shape characteristics of the weld pool; therefore, using welding current and wire filler ratio as control variables of the welding system is correct.

[0182] S35. Using the least squares identification method and the final prediction error criterion, the model structure of the nondeterministic noise Hammerstein stochastic system model of the ship's GMAW welding dynamic process is optimized and identified, thereby constructing the state-space equation for particle filter welding forming prediction.

[0183] After determining the pure delay coefficients of the two welding process parameters, and assuming that the order of the linear subsystem is known and determined, the highest power of the nonlinear subsystem is identified. The goal is to find an error index function that reduces and smooths out the error. This identification order is based on the polynomial approximation theory of nonlinear components (the essence of nonlinearity is a polynomial): the larger the highest power p, the better the accurate approximation. The error should be minimized when p equals the true power of the system, and theoretically, further increases in p will not decrease the error. However, the value of p in a real welding system is uncertain and can be very large. Therefore, a satisfactory error level can be obtained by increasing the linear order.

[0184] First, assuming the order of the linear subsystem is known, we take k = k0+1, ..., k0+N (N≥l+p×(m+1)) for the time-domain expression of the nondeterministic noisy Hammerstein stochastic system model, and obtain the least squares normal equation:

[0185]

[0186] Error criterion function:

[0187]

[0188] Taking the minimum value of the error criterion function, the least squares solution is obtained as follows:

[0189]

[0190] Model parameter correspondence

[0191]

[0192] The above algorithm becomes increasingly slower as the amount of data increases, and excessive old information diminishes the effectiveness of new information. Considering the real-time nature of the model structure, a recursive least squares identification method is adopted. The least squares normal equation for N sets of observation data is assumed to be: When the N+1th set of data is measured At that time,

[0193]

[0194] assumed The recursive formula is:

[0195]

[0196] The above formula can be simplified to:

[0197]

[0198] The initial value for recursion can be selected as follows:

[0199]

[0200] The final error criterion of the recursive algorithm:

[0201]

[0202] Where ε = 10 -5 .

[0203] As the Hammerstein model principle indicates, the knowledge model for ship GMAW welding processes is not only structurally complex, but the current characteristic output of the weld pool is also related not only to the current welding process parameters input, but also to the input parameters from previous historical moments, and further to random system disturbances from those historical moments. This embodiment uses the weld pool characteristic dimension – frontal weld width W – as an example. f As system outputs, the system inputs consist of welding process parameters – welding current I and wire filler ratio V. f To represent, the state-space equation for welding forming prediction can be expressed mathematically using the Hammerstein random noise model as:

[0204]

[0205] In the formula, Represents the output width W f ;

[0206] and These represent the input welding current and the wire fill rate, respectively.

[0207] e(k) is the equivalent composite noise;

[0208] l represents the order of the historical moment of the output parameter melt width in the linear subsystem;

[0209] m1 and m2 are the orders of welding current and wire fill rate in the linear subsystem, respectively;

[0210] p1 and p2 are the highest powers of the welding current and wire fill rate in the nonlinear link, respectively.

[0211] d1 and d2 are the pure delay coefficients of welding current and wire fill rate in the nonlinear link, respectively.

[0212] and These are the structural coefficients for welding current and wire fill rate in the nonlinear process, respectively.

[0213] α i The order factor representing a historical moment in the melting point width;

[0214] and These represent the order coefficients of the welding current and the wire fill rate in the linear subsystem, respectively.

[0215] Based on a structural identification method using knowledge modeling of the welding dynamic process, the spatial state structural parameters of the weld pool width, welding current, and wire filler ratio are optimized. First, the pure delay coefficients d1 and d2 are determined using step tests. Second, assuming the orders m1 and m2 of the linear subsystem, the optimal highest power value is identified by sequentially increasing the nonlinear powers p1 and p2 using the recursive least squares method. Finally, the minimum loss function is found based on the final prediction error criterion FPE, thereby determining the optimal orders m1 and m2 of the linear subsystem. The specific identification approach is detailed below. Figure 5 .

[0216] First, based on the step response experiment of welding current and wire fill rate, it is known that the time delay characteristics of the GMAW welding dynamic process are not obvious and the pure delay coefficients d1 and d2 are both less than 1. Therefore, the pure delay coefficients d1 and d2 of the nonlinear welding current and wire fill rate are both selected as 0. In this embodiment, the particle filtering method is used to build a molten pool feature prediction model. The prediction process conforms to a first-order Markov process, that is, the order l = 1 of the historical moment of the output parameter weld width in the linear subsystem. Second, adhering to the principle of timeliness, the structural model should not be too complex. It is assumed that the order m1 = m2 = 2 of the welding current and wire fill rate in the linear subsystem. The highest power p1 and p2 of the optimal nonlinear welding current and wire fill rate are determined by the recursive least squares method. Finally, the linear order is changed sequentially according to the optimal highest power, and the minimum loss function is found using the final prediction error criterion to determine the optimal linear order m1 and m2. Through the above structural identification of the forming state, the state-space equation with optimized structural parameters is finally provided for the particle filtering forming prediction model.

[0217] S4, Bayesian welding state tracking training: The welding information after preprocessing in step S2 is divided into training set and test set to provide data support for Bayesian welding state tracking training and welding formation prediction. Bayesian filtering is used to perform state tracking training on the state space equation of the welding formation prediction. Minimum variance-unbiased (MVU) estimation is used to optimize parameters, and then a particle filter-based dynamic forming prediction model for ship hull structure welding is constructed.

[0218] In this embodiment, the method for dividing the preprocessed welding information from step S2 into a training set and a test set in step S4 is as follows: The preprocessed welding information from step S2 is used as the original dataset to establish a Bayesian tracking training model to determine the parameters of the state equation. The first S sets of data from the preprocessed original historical dataset AX are used as the training set AT for state tracking training, i.e., AT = AX(1:S, :) = [ATI, ATV, ..., ATB, ATD, ...], where ATI, ATV, ATB, and ATD represent the tracking of welding current, wire fill rate, and corresponding weld width and penetration depth, respectively. The dataset TX, after the S groups of the preprocessed original dataset AX, is used as the test set for comparison between the true and predicted values. That is, TX = OX(:, S+1:N) = [TXI, TXV, ..., TXB, TXD, ...]. Bayesian theory is used to train and model the test set AT using state tracking. The MVU is used to estimate the optimal model parameters that minimize the error between the algorithm's predicted values ​​and the experimental true values. Specifically, the RMSE or goodness of fit is used as the evaluation index, and the condition that it does not exceed the set constraint deviation Error is met, thereby improving the state space equation of welding forming prediction.

[0219] S5, Nonlinearization of Welding Dynamic System, Initialization of Sampling Particles and Corresponding Weights: The nonlinear welding process is defined using a particle filter-based prediction model for the dynamic forming of hull structure welding. Monte Carlo sampling of the welding forming state is achieved by recursively estimating the forming state through particle filtering. Since the posterior probability density function is unknown, the importance probability density function is selected to satisfy the Monte Carlo sampling, thereby approximating the particle set.

[0220] Specifically, step S5 includes:

[0221] S51, Assume that the welding nonlinear system can be defined as a time-varying sequence of welding forming states x k and a set of observation sequences z k Composition of dynamic system model:

[0222] x k =f(x) k-1 w k (State Transition)

[0223] z k =h(x k v k (Observation equation)

[0224] In the formula, x k and z kThese represent the weld formation state (weld width, weld reinforcement, and weld depth, etc.) and process (welding current, arc voltage, welding speed, and wire filler ratio, etc.) observation information at time k, respectively. f(*) and h(*) represent the forming state transition and process observation functions, respectively. k and v k Let k be the system's independent random disturbance noise and observation noise at time k;

[0225] Assuming the weld formation state x k It follows a first-order Markov process, and simultaneously welds to the formed state x. k With process observation information z k Independent of each other, from the perspective of Bayesian theory, the welding state estimation problem is based on the process observation information z from the previous series of time steps. 1：k (Posterior knowledge) Recursively calculate the current welding state x k Credibility p(x) k |z 1：k It requires two steps: forming a recursive prediction and observational correction and updating, to perform the above recursion.

[0226] (1) Forming recursive prediction

[0227] x 0：k ={x i Let i = 0, 1, ..., k represent the welding forming state variables from time 0 to time k, and z 1：k ={z1, z2, ..., z k} represents the process observation information corresponding to times 1 to k, and assumes that the posterior probability density function of the welding forming state from time 0 to k-1 is p(x). 0：k-1 |z 1：k-1 Given that the predicted probability density function of the weld formation state at time k is calculated according to the Chapman-Kolmogorov theoretical formula, i.e.

[0228]

[0229] (2) Observation correction and update

[0230] Using welding process observation information z from time 0 to k 1：k The likelihood probability density function p(z) 1：k |x 0：k Estimate the probability of the weld formation state, and based on Bayesian theory, determine the marginal probability p(z) given the known process observation information. 1：k ) and the edge probability of the formed state p(x) 0：k Estimate its posterior probability distribution p(x) under the condition of ) 0：k |z 1：k ):

[0231]

[0232] Among them, the marginal probability p(z) of the welding known process observation information 1：k () is the normalization constant:

[0233] p(z 1：k )=∫p(z 1：k |x 0：k )p(x 0：k )dx 0：k .

[0234] In the welding forming prediction model architecture, due to the highly complex calculus calculations involved, it is difficult to handle the problem using the recursive operation of forming recursive prediction-observation correction update. To address the complex recursive operation problem in the optimal Bayesian filtering algorithm, a Monte Carlo random sampling method is introduced to replace the calculation of posterior probability. The basic idea is that when solving a problem involves the probability of an event occurring at a certain random time or the expected value of a random variable, the probability of the event occurring at that time is approximated by the frequency of the event, or certain numerical characteristics of the random variable are obtained and used as the solution to the problem.

[0235] Assume that the posterior probability p(x) can be obtained n |z 1：k n independent and identically distributed samples {x} were sampled from the sample. (i) If the integers are i = 1, 2, ..., n (n ≥ 1), then the approximate estimate of the posterior probability can be expressed as:

[0236]

[0237] In the formula, δ(x) is the Dirac function;

[0238] The Monte Carlo method is used to directly estimate the expected value of the posterior probability density:

[0239]

[0240] According to the Strong Law of Large Numbers (SLLN), we know that...

[0241]

[0242] According to the central limit theorem, the convergence rate is expressed as:

[0243]

[0244] In the formula, Let f(x) be the variance. From this, we can obtain the order of the error of the Monte Carlo integration method: O(N). 1 / 2 It is independent of the dimension of the integral and is suitable for solving complex high-dimensional integrals.

[0245] S52, Monte Carlo sampling of welding forming state: In the welding forming prediction model architecture, since the posterior probability density function is unknown, the importance probability density function is selected to satisfy Monte Carlo sampling.

[0246] S6, Sequential Importance Sampling: Assuming the prior probability distribution is used as the importance probability density function, i.e. the proposal distribution guides the particles to perform sequential importance sampling, and then recursively calculates the importance weight of the sampled particles.

[0247] S7, Resampling Strategy: Measure the degree of weight degradation and determine whether resampling is needed. If so, resample the particles according to the particle weight iteration value and normalize the particle weight to obtain the prediction result of the ship GMAW weld formation at the current moment.

[0248] S8, steps S5-S7 constitute one iteration of the state estimation process of the traditional particle filter method; repeat steps S6-S7 to output the prediction results of the ship GMAW weld formation at different times in sequence.

[0249] The specific implementation method of step S6 includes:

[0250] Posterior probability density p(x) k |z 1：k Since it is not always possible to provide an analytical expression, it is difficult to directly extract samples from the distribution. Therefore, the Sequential Importance Sampling (SIS) method is needed to solve the sampling difficulty problem.

[0251] Assuming a known reference distribution π(x) 0：k |z 1：k Draw a set of n independent and identically distributed particles {x} (i) , i = 1, 2, ..., n} (n ≥ 1), when the number of particles n → ∞, the reference distribution π(x 0：k |z 1：k It highly approximates the posterior probability density function p(x) 0：k |z 1：k It can be decomposed into a recursive form:

[0252] π(x 0：k |z 1：k )=π(x 0：k-1 |z 1：k-1 )π(x k |x 0：k-1 , z 1：k )

[0253] Introducing the importance probability density function π(x) k |x 0：k-1, z 1：k Helps solve complex high-dimensional integral problems in Monte Carlo simulations.

[0254]

[0255] The importance sampling process involves sampling particles at time k. Update the state estimate at time k-1:

[0256]

[0257] The importance weight at time k is:

[0258]

[0259] in

[0260]

[0261] In actual calculations, the particle ensemble The sample can be obtained according to the following formula:

[0262]

[0263] Recursive importance weights

[0264]

[0265] Assume an importance distribution in sequential importance sampling. satisfy:

[0266]

[0267] The recursive sequential importance sampling weight is:

[0268]

[0269] Normalize the importance weights

[0270]

[0271] Finally, the posterior probability density function of sequential importance sampling (SIS) is calculated, i.e.

[0272]

[0273] in, The importance probability density function The normalized weights of several sampled particles, where δ(*) represents the Dirac function.

[0274] The specific implementation plan for step S7 includes:

[0275] Steps S5-S7 constitute one iterative process for predicting and estimating the welding forming state using the traditional particle filtering method. However, after several iterations of sequential importance sampling, the weights of some particles may become negligible. This degradation phenomenon is unavoidable due to inherent limitations of the algorithm. Therefore, to reduce the impact of particle degradation, an importance resampling strategy is introduced. Essentially, this strategy increases particle diversity, retains and replicates sample points with high weights to adapt to the dynamic process modeling of the system, thereby suppressing degradation. Figure 6 A schematic diagram of the resampling process in the particle filter algorithm is given. To determine whether a resampling process is necessary, the degree of weight degradation needs to be assessed, and the following effective sampling scale N needs to be calculated. eff

[0276]

[0277] Effective sampling scale N eff To measure the degree of degradation of particle weights, a larger value indicates a greater gap between particle weights, signifying more severe weight degradation. When it exceeds a certain threshold N... thre At that time, a set of n particles is regenerated through a resampling strategy. Make And assign weights to each new particle.

[0278] Finally, the posterior probability density function of the Sequential Importance-Resampling (SIR) method is calculated, meaning the shaped state of the standard particle filter method can be estimated as follows:

[0279]

[0280] Traditional particle filtering methods are simple in structure and easy to implement. Under optimal estimation, the approximate estimate converges to the true state value. However, in practical engineering applications, this method still has certain defects and shortcomings, mainly in the following two aspects: (1) The standard particle filtering method introduces an importance probability density distribution in the sequential importance sampling process, which causes the particle weight variance to accumulate continuously with the increase of the algorithm iteration number. At the same time, the importance weights corresponding to most particles also tend to zero, i.e., particle degeneration. This leads to a serious waste of computing resources, and also makes the approximate estimate unable to accurately describe the posterior distribution of the true state. More seriously, this degeneration phenomenon cannot be avoided due to the defects of the method itself. (2) Resampling strategy is an effective and important means to improve the particle degeneration phenomenon. By resampling the discrete approximate posterior probability distribution obtained by importance sampling, the samples with larger weights are copied multiple times under the guidance of the particle motion and the distribution of the state at the previous moment, thereby increasing the number of effective particles and achieving the purpose of suppressing degeneration. At the same time, the resampling process may cause some low-weight particles to be discarded or lost, causing the resampled particles to move away from the true state posterior region too early, resulting in sample impoverishment, which ultimately leads to an increase in the variance of state estimation and a significant decrease in filtering performance.

[0281] The second embodiment of this invention adopts the particle filtering method based on state trajectory clustering similarity (hereinafter referred to as the improved filtering method) disclosed in Chinese invention patent application No. 202310000323.X. That is, it uses the clustering similarity method to perform distance discrimination measurement on the system's real and sampled particle state information sets, including filtering of the current (stage) state and measurement of measurement information for future multi (stage) state prediction. This guides the generation and improvement of new proposal distributions, thereby updating the weight calculation of the importance sampling process. This overcomes the inherent defect of the traditional PF method, which uses a prior probability distribution instead of the importance probability density function, effectively improves the particle degradation phenomenon, and significantly improves the accuracy and robustness of the estimation method. At the same time, the algorithm process abandons the resampling strategy in the traditional PF method for the purpose of improving the particle degradation phenomenon, fundamentally solves the particle degradation problem, and effectively improves the efficiency of the method.

[0282] Please see Figure 7 The second embodiment of the present invention provides a method for predicting the formation of GMAW weld seams in ships based on clustering similarity particle filtering, comprising the following steps:

[0283] S1, Construction and test design of the experimental platform for the GMAW welding system of the hull structure: The experimental platform for the GMAW welding system of the hull structure is constructed. Welding orthogonal tests are designed to obtain welding process parameters that meet the forming specifications. Then, corresponding test schemes for weld tracking and real-time acquisition of molten pool are formulated.

[0284] S2, Real-time acquisition and preprocessing of welding information during welding formation: During the weld tracking and real-time acquisition of the molten pool test, image information is acquired in real time based on the molten pool image sensor and the geometric features of the image are extracted to obtain the weld size online in real time. The welding current and arc voltage are acquired through the Hall sensor, and the wire filling rate is acquired through the welding machine. The acquired welding information is preprocessed, including welding current, arc voltage and wire filling rate.

[0285] S3, the architecture of the state-space equation for particle filter welding forming prediction, includes the following steps:

[0286] S31, Analyze and determine the type of interference noise;

[0287] S32, Based on the determined type of interference noise, establish a nondeterministic noise Hammerstein stochastic system model for the dynamic process of ship GMAW welding;

[0288] S33, perform structural parameter identification analysis on the nondeterministic noise Hammerstein stochastic system model of the ship's GMAW welding dynamic process;

[0289] S34. Design a welding process step response test to obtain the transfer function and corresponding parameters of the weld pool shape under positive / negative step conditions of welding current and wire filler rate, so as to provide a basis for model structure optimization and identification.

[0290] S35, using the least squares identification method and the final prediction error criterion, the model structure of the nondeterministic noise Hammerstein stochastic system model of the ship GMAW welding dynamic process is optimized and identified, thereby constructing the state space equation for particle filter welding forming prediction.

[0291] S4, Bayesian welding state tracking training: The welding information after preprocessing in step S2 is divided into training set and test set to provide data support for Bayesian welding state tracking training and welding formation prediction. The Bayesian filter trained by state tracking is used to optimize the parameters of the state space equation of the welding formation prediction, and then a dynamic forming prediction model of ship structure welding based on particle filter is constructed.

[0292] S5, Nonlinearization of welding dynamic system, initialization of sampling particles and corresponding weights: The nonlinear welding process is defined by using a particle filter-based prediction model for the dynamic forming of hull structure welding. Monte Carlo sampling of the welding forming state is realized by recursive prediction of forming and observation correction and update. Since the posterior probability density function is unknown, the importance probability density function is selected to satisfy the Monte Carlo sampling, thereby approximating the particle set.

[0293] S6, Sequential Importance Sampling: Assuming the prior probability distribution is used as the importance probability density function, that is, the proposal distribution guides the particles to perform sequential importance sampling, and then recursively calculates the importance weight of the sampled particles.

[0294] S7, Clustering similarity measurement of welding forming state trajectory similarity: Through state space joint trajectory feature mining and vector planning, clustering analysis method is used to measure the similarity of measurement information predicted by the current stage SIS filtering (Sequential Importance Sampling, SIS) and the future multi-stage Gaussian Particle Filtering (GPF).

[0295] S8, Correcting the importance probability density function: Using the similarity metric from step S7 to guide the generation of a new proposal distribution, thereby updating the importance probability density function in step S6 to compensate for the correction of the Monte Carlo sampling process;

[0296] S9, Update Markov Importance Weights: Update the importance weights of the first-order Markov model in step S6 using the proposed distribution corrected in step S8, and normalize the particle weights to obtain the prediction results of the welding forming state at the current moment.

[0297] S10, steps S5-S9 constitute an iterative process for predicting and estimating the welding forming state using a particle filtering method based on state trajectory clustering similarity; repeat steps S5-S9 to sequentially output the prediction results of ship GMAW weld forming using clustering similarity particle filtering.

[0298] In the second embodiment of the present invention, steps S1-S6 are the same as in the first embodiment, and will not be repeated here for brevity; the improved filtering method of steps S6-S10 can be found in the particle filtering method based on state trajectory clustering similarity disclosed in Chinese invention patent application No. 202310000323.X.

[0299] Specifically, step S7 includes:

[0300] S71, Feature Mining and Vector Programming of Joint State-Space Trajectory (Normal and Corrected Trajectories):

[0301] The set of particles representing the joint trajectory of the welding forming state from time k to k+L+l is selected as... in Follows the SIS filtering process, x′ j(i) It follows the GPF prediction process, where L is the length of the filtered trajectory and l is the length of the predicted trajectory. Since the actual welding forming state of the system is unknown, the consistency of the forming state trajectory is characterized by the process observation likelihood function. The corresponding likelihood trajectory is solved by the process observation equation based on the forming state trajectory of the sampled particles. in

[0302]

[0303] Observation noise v k =0, the observation equation H(*) is a known function determined by a specific research object under conditions of no noise interference.

[0304] S72, Similarity Measurement of Actual Welding Formation State and Particle Process Observation Likelihood Trajectory: The method for measuring the similarity between the measurement information predicted by the current stage filtering and the future multi-stage Gaussian filtering using cluster analysis is as follows: The process observation likelihood trajectory corresponding to the actual welding system formation state is {Z}. k}={z j :j=k,…,k+L+l}, spatial trajectory clustering consistency analysis is used, and distance similarity metric is selected to measure the distance similarity between the actual welding forming state and the particle process observed likelihood trajectory. The calculation is as follows:

[0305]

[0306] Where dis(*) represents the distance similarity function, and dis(*)≥0, ξ is the metric type parameter;

[0307] To enhance the reliability of the algorithm's output, an exponential function structure is used to perform an exponential transformation on the above equation to obtain the updated similarity metric D. k (i)

[0308] i = 1, ..., n

[0309] Where λ is the reliable gradient factor.

[0310] In step S8, the similarity metric from step S7 is used to guide the generation of a new proposal distribution, thereby updating the importance probability density function in step S6 to compensate for the correction Monte Carlo sampling process.

[0311] Step S8 includes: based on the distance similarity measure between the process observation likelihood trajectory and the measured likelihood trajectory of the sampled particles obtained in step S72, applying the similarity correction formula to the prior probability distribution p(x) according to the following formula. k |x k-1 The importance of substitution probability density function π(x) k|x 0：k-1 , z 1：k ):

[0312] π(x k |x 0：k-1 , z 1：k ) = D k *p(x k |x k-1 ).

[0313] S9, Update Markov Importance Weights: Update the importance weights of the first-order Markov model in step S6 using the proposed distribution corrected in step S8, and normalize the particle weights to obtain the prediction results of the welding forming state at the current moment.

[0314] The importance weights of the first-order Markov model in step S6 are calculated using the revised proposal distribution from step S8, and the importance weights of the forming states at times k and k+L+l are obtained respectively. and The calculation is as follows:

[0315] i = 1, ..., n

[0316] i = 1, ..., n

[0317] Where, p v (*) represents the probability density function of the likelihood function for welding process observation;

[0318] The importance weights are normalized according to the following formula:

[0319]

[0320]

[0321] Based on the above theory, the improved filtering algorithm process is as follows:

[0322]

[0323] Wherein, the particle distribution at time k follows the shaped state sampled by SIS filtering. Its corresponding importance weight It can approximately characterize the posterior probability density function p(x) of the state. k |z 1：k The particle distribution of the formed state at time k+L+l follows the GPF prediction sampling. Its corresponding importance weight The prediction probability density function p(x) can be approximately represented. k+L+l |z 1：kTherefore, the estimated forming state value x at the current moment. k The estimated value of the future forming state x can be obtained through filtering. k+L+l This can be obtained through the prediction step. The improved algorithm is implemented as follows:

[0324] • Forming recursive prediction

[0325] The steps are consistent with the SIS (GPF) filtering (prediction) process, sampling to obtain the set of particles in the weld formation state.

[0326] • Observation update correction

[0327] The first-order Markov process is updated by using the similarity metric between the current filtering (current trajectory) and the future multi-stage Gaussian prediction (corrected trajectory) of welding process measurement information, and then the importance weight of the corresponding forming state is obtained. and And normalize it to obtain and

[0328]

[0329]

[0330] The above steps constitute one iteration of the ship GMAW weld formation prediction model based on cluster similarity particle filtering. Unlike traditional particle filtering algorithms, this algorithm consists of formation prediction (filtering) - observation update - filtering (prediction), without a resampling step. The specific algorithm steps are shown in Table 4.

[0331] Table 4. Prediction process of ship GMAW weld formation using clustering similarity particle filtering.

[0332]

[0333]

[0334] Convergence of Cluster Similarity Particle Filtering: The improved algorithm, Cluster Similarity Particle Filtering, fully satisfies the Bayesian state estimation principle in Bootstrap Filtering theory. It can be implemented using its weighted bootstrap method: Assuming a set of state combination trajectories... The probability distribution follows a continuous probability density function G(x), and the posterior probability distribution obtained by the improved algorithm is proportional to G(x)W(x) with constant coefficients, and W(x) is a known corresponding weight function. Referring to the observation correction and update formula in S51, the posterior probability density of the state p(x) is... k |z 1：k ) and the observed likelihood probability density function p(z) k |xk ) and predicted probability density p(x) k |z 1：k-1 The product of ) is proportional to a constant, where G(x) can be regarded as the state prediction probability density function p(x) k |z 1：k-1 Referring to the S9 importance weight formula W(x), it can be equivalent to the observation likelihood function p(z). k |x k The product of the distance similarity metric and the sample number n→∞. Then, from the trajectory set... and the corresponding normalized weights The discrete distribution of the constituent particles can approximate the true posterior probability density distribution, which clearly shows that the method conforms to the Boostrap Filtering theory and the results are reasonable and effective.

[0335] This invention also verifies the effectiveness of the ship GMAW weld formation prediction method based on traditional and clustering similarity particle filtering through simulation experiments. Following the state tracking training parameter identification process for the dynamic process of GMAW welding of ship hull structures, several sets of data under the experimental process conditions in Table 1 were selected as the original welding test dataset AX. Simulations were performed comparing the traditional particle filter (PF), auxiliary particle filter (APF), and clustering similarity particle filter (CSPF) methods. AT was selected as the training set for state tracking, and TX as the test set for weld formation prediction. According to the state space equation for weld formation prediction in step S35, where the state tracking noise is... And R k =1, select the number of sampled particles N=200, the number of tracking steps k=1,2,...,S and S=120, the number of prediction steps k=S,S+1,...,X and X=200. In the improved algorithm CSPF, the filter trajectory length L=2, the prediction trajectory length l=1, the reliable gradient factor λ=-1, and the number of simulations T=200. The computer processor used has a speed of 3.40GHz and a random access memory of 16.0GB. This invention uses two spatial distance similarity measures for clustering similarity, where CCSPF represents the Chebyshev spatial distance similarity algorithm (measure type parameter ξ=∞) and ECSPF represents the Euclidean spatial distance similarity algorithm (measure type parameter ξ=2). The absolute error AE and the root mean square error RMSE are selected as evaluation measures of the state tracking performance level of different methods, x tur and x est The distribution represents the true value of the experiment and the estimated state value, i.e.

[0336]

[0337]

[0338] (1) Comparison of training effects on welding process status tracking

[0339] The state tracking results of the four methods are as follows Figure 8 As shown in Table 5, to comprehensively demonstrate the comparative results of state tracking training for various algorithms, the quantitative comparison of state tracking results obtained from 200 simulations is presented. The state tracking performance metrics include absolute error (AE), variance (the sum of squares due to error, SSE), mean squared error (MSE), root mean squared error (RMSE), and R_square (Coefficient of determination). The closer AE, SSE, MSE, and RMSE are to 0, and the closer R_square is to 1, the better the state tracking performance.

[0340] Depend on Figure 8 It can be seen that the state tracking effects of the four methods are good, and they can all relatively completely approximate the real change trend of weld formation under different welding process conditions. They can also accurately extract the forming change law implied in the AT part of the state tracking set, and provide accuracy guarantee for the test set TX to maintain the same mechanism. As shown in Table 5, the state tracking effect index of the improved filtering method CSPF of this invention is significantly better. Taking ECSPF as an example, SSE is improved by 55% and 46% compared with PF and APF, respectively; MSE is improved by 54% and 46% compared with PF and APF, respectively; RMSE is improved by 33% and 25% compared with PF and APF, respectively; and R_square is improved by 27% and 20% compared with PF and APF, respectively. It can also be concluded that the Chebyshev distance similarity CCSPF has the best state tracking training effect and strong stability.

[0341] Table 5 Comparison of the average performance of four nonlinear prediction models after 200 state tracking runs.

[0342]

[0343] (2) Comparison of weld formation prediction accuracy

[0344] The weld formation prediction results of the four methods are as follows: Figure 9As shown in Table 6, to comprehensively demonstrate the accuracy comparison of welding formation prediction using various algorithms, a quantitative comparison of the formation prediction results obtained from 200 simulation calculations is presented. The evaluation indicators for the accuracy of the formation prediction include the absolute error AE, the average RMSE, and the variance of RMSE.

[0345] Table 6 Comparison of the average performance of the four nonlinear models in predicting the forming accuracy after 200 runs.

[0346]

[0347] Note:RMSE Mean=the mean of RMSE,RMSE Variance=the variance of RMSE.

[0348] Depend on Figure 9 As shown in Table 6, the predicted trends of the four methods are basically consistent with the actual state of the test set TX. The mean root mean square error of the prediction results is maintained below 0.88 mm, indicating that the particle filtering method has a certain degree of well-posedness in knowledge modeling applications such as state tracking and forming prediction of the dynamic process of GMAW welding of ship hull structures. Compared with the PF and APF methods, the improved CSPF predicts trends closer to the welding forming characteristic curve. The absolute errors AE, RMSE, and the mean RMSE (variance) of the prediction results are all significantly reduced. Taking CCSPF as an example, the mean RMSE of the forming prediction results is reduced by 46% and 44% respectively, indicating that the improved CSPF method has higher forming prediction accuracy. The mean RMSE curve is relatively stable, and its variance is reduced by about 280 times and 260 times respectively. This indicates that the particle set representing the state of the forming prediction result of the improved CSPF algorithm has the smallest dispersion, the lowest degree of uncertainty expression, and stronger robust stability.

[0349] (3) Comparison of the timeliness of prediction of welding forming state

[0350] Under the same known time setting, the accuracy level of the state estimation results of different algorithms for forming prediction was obtained by adjusting the number of sampling particles N. This was used to obtain and compare the corresponding computational costs to verify the timeliness of the improved algorithm CSPF, as detailed in Table 7. Table 7 shows that, under the same computational cost, the improved filtering algorithm CSPF uses the fewest sampling particles N, while its forming prediction accuracy is significantly higher than that of PF and APF methods, increasing by approximately two times. This verifies that the improved filtering algorithm CSPF has high computational efficiency and outstanding timeliness advantages.

[0351] Table 7 compares the timeliness of four nonlinear prediction models after 200 runs in the same computation time.

[0352]

[0353] Note: N=the number of particles sampled, RMSE Mean=the mean of RMSE, RMSE Variance=the variance of RMSE, AVG=average.

[0354] This invention, through random simulation experiments of ship hull structure GMAW using different methods, demonstrates that particle filtering and its improved methods can meet the requirements of ship welding processes in terms of state tracking training effect and weld formation prediction accuracy. Furthermore, combined with the convergence of the improved algorithm, cluster similarity particle filtering exhibits advantages such as better state tracking effect, higher forming prediction accuracy, stronger robustness, and better timeliness in the application of ship hull structure GMAW process knowledge modeling.

[0355] By adopting the above technical solution, the present invention has the following beneficial effects:

[0356] (1) Stochastic theoretical framework of ship GMAW process noise

[0357] The GMAW welding process in marine applications is subject to various random and uncertain disturbances, such as unstable welding power supply output, weld gap variations, uncertain ambient temperature, thermal deformation, and heat accumulation. These factors introduce uncertainty into the welding system's operation, meaning the state of the weld pool will change under the influence of random factors. Currently, most artificial intelligence modeling methods are based on deterministic system theory, where the relationship between input and output is strictly corresponding. The process of obtaining the output from the model generally does not consider the influence of time-varying processes or other disturbances within the system. Therefore, this invention employs a stochastic theoretical model to describe the dynamic system of ship welding, which is more consistent with the actual process. Addressing the knowledge modeling problems related to the nonlinearity, time delay, multivariate coupling, uncertainties, and random disturbances in ship GMAW welding, this invention introduces a stochastic process mechanism to establish a nondeterministic, nonlinear Hammerstein noise model between welding specification parameters and weld pool shape parameters. This model accurately reflects the characteristics and effects of random noise in the actual welding process. Based on online constant specification step response tests and identification techniques such as recursive least squares and final prediction error criteria, the noise model structure is identified and optimized to obtain the state-space equation characterizing the welding formation mechanism. The model obtained by this method will better conform to the welding formation law when describing the dynamic system of ship welding. This provides theoretical support and accuracy assurance for knowledge modeling of the particle filter welding dynamic process, thereby improving the accuracy of ship GMAW weld formation prediction.

[0358] (2) Knowledge Modeling for Weld Formation Prediction Using Particle Filtering

[0359] Particle filtering has unique advantages in handling state estimation problems of non-Gaussian, nonlinear time-varying systems and random noise interference. This invention is the first to apply this method to knowledge modeling of the GMAW welding process in ships. Particle filtering is used to establish a dynamic knowledge model of the GMAW process in ships under the combined effects of nonlinear system process input and random noise interference. This method abandons previous modeling methods that relied heavily on prior knowledge, expert experience, and hardware testing techniques, incorporating a large number of subjective factors and input technical parameters. It fully leverages the advantages of particle filtering to deeply mine and reveal the temporal changes of welding process laws and weld formation mechanisms, i.e., the time dynamic relationship between welding process parameters and molten pool geometry. It also maintains the accuracy of output response results with fewer model inputs, significantly reducing the requirements for welding platform sensor hardware and model computation and operation costs. Simulation results show that the state tracking training effect is good, ensuring accurate extraction of the characteristic parameters related to the formation mechanism implicit in the tracking set; the predicted weld formation trend is consistent with the actual change curve of the test set, and the accuracy is maintained within 0.88mm. Therefore, the proposed method for predicting the weld formation of ship GMAW based on traditional particle filtering can meet the requirements of ship welding process in terms of state tracking training effect and weld formation prediction accuracy. This shows that the particle filtering method has certain applicability in the application of dynamic knowledge modeling in GMAW, and also provides a technical basis for monitoring the weld formation quality in the ship GMAW welding process.

[0360] (3) Application of improved particle filtering method in welding process modeling

[0361] The particle filtering method based on state trajectory clustering similarity improves the particle filtering method itself without relying on external methods, and restructures the algorithm logic framework: Addressing the particle degeneration phenomenon caused by unknown and assumed prior probability distributions, the particle filtering algorithm serves as the core modeling framework and theoretical analysis basis. It utilizes SIS and GPF methods to obtain corrected trajectories combining current and future multi-stage spatial state information, and performs clustering analysis—distance similarity measurement—with the system's true state trajectory. Higher consistency similarity indicates a closer representation to the true state, guiding the generation of new proposed distributions to improve particle degeneration. Simultaneously, the first-order Markov process is updated to compensate for the revised importance weight calculation. By selectively integrating the updated compensation scheme (clustering metric) into the latest phased measurement information during the importance sampling process to replace the resampling process, the particle depletion problem can be fundamentally eliminated, and timeliness is significantly improved. Based on the convergence theorem proof of the improved algorithm CSPF, and through experimental verification, CSPF has advantages over traditional PF and APF in the application of knowledge modeling of GMAW process for ship hull structures, such as better state tracking effect, higher forming prediction accuracy, stronger algorithm robustness, and faster timeliness.

[0362] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit of the present invention should fall within the patent scope covered by the present invention.

Claims

1. A particle filtering-based method for predicting the formation of GMAW weld seams in marine applications, characterized in that, Includes the following steps: S1, Construction and test design of the experimental platform for the GMAW welding system of the hull structure: The experimental platform for the GMAW welding system of the hull structure is constructed. Welding orthogonal tests are designed to obtain welding process parameters that meet the forming specifications. Then, corresponding test schemes for weld tracking and real-time acquisition of molten pool are formulated. S2, Real-time acquisition and preprocessing of welding information during welding formation: During the weld tracking and real-time acquisition of the molten pool test, image information is acquired in real time based on the molten pool image sensor and the geometric features of the image are extracted to obtain the weld size online in real time. The welding current and arc voltage are acquired through the Hall sensor, and the wire filling rate is acquired through the welding machine. The acquired welding information is preprocessed, including welding current, arc voltage and wire filling rate. S3, the architecture of the state-space equation for particle filter welding forming prediction, includes the following steps: S31, Analyze and determine the type of interference noise; S32, Based on the determined type of interference noise, establish a nondeterministic noise Hammerstein stochastic system model for the dynamic process of ship GMAW welding; S33, perform structural parameter identification analysis on the nondeterministic noise Hammerstein stochastic system model of the ship's GMAW welding dynamic process; S34, Design a welding process step response test to obtain the transfer function and corresponding parameters of the weld pool shape under positive / negative step conditions of welding current and wire filler rate, so as to provide a basis for model structure optimization and identification; S35, using the least squares identification method and the final prediction error criterion, the model structure of the nondeterministic noise Hammerstein stochastic system model of the ship GMAW welding dynamic process is optimized and identified, thereby constructing the state space equation for particle filter welding forming prediction. In step S35, the weld pool feature size is calculated as follows: front weld width As the system output, the system input uses welding process parameters - welding current. and wire filler ratio To represent; and the mathematical expression of the state-space equation for the predicted welding forming is: In the formula, Represents the output width ; and These represent the input welding current and the wire fill rate, respectively. This is the equivalent composite noise; The order of the historical moment of the output parameter melt width in the linear subsystem; and These represent the orders of the welding current and wire fill rate in the linear subsystem, respectively. and These are the highest powers of the welding current and wire fill rate in the nonlinear process, respectively. and These are the pure delay coefficients for welding current and wire fill rate in the nonlinear process, respectively. and These are the structural coefficients for welding current and wire fill rate in the nonlinear process, respectively. The order factor representing a historical moment in the melting point width; and These represent the order coefficients of the welding current and the wire fill rate in the linear subsystem, respectively. For time step; S4, Bayesian welding state tracking training: The welding information after preprocessing in step S2 is divided into training set and test set to provide data support for Bayesian welding state tracking training and welding formation prediction. The Bayesian filter trained by state tracking is used to optimize the parameters of the state space equation of the welding formation prediction, and then a dynamic forming prediction model of ship structure welding based on particle filter is constructed. S5, Nonlinearization of welding dynamic system, initialization of sampling particles and corresponding weights: The nonlinear welding process is defined by using a particle filter-based prediction model for the dynamic forming of hull structure welding. Monte Carlo sampling of the welding forming state is realized by recursive prediction of forming and observation correction and update. Since the posterior probability density function is unknown, the importance probability density function is selected to satisfy the Monte Carlo sampling, thereby approximating the particle set. S6, Sequential Importance Sampling: Assuming the prior probability distribution is used as the importance probability density function, that is, the proposal distribution guides the particles to perform sequential importance sampling, and then recursively calculates the importance weight of the sampled particles. S7, Clustering Similarity Measurement of Welding Formation State Trajectory Similarity: Through state space joint trajectory feature mining and vector planning, clustering analysis is used to measure the similarity of measurement information between the current stage sequential importance sampling and the future multi-stage Gaussian filter prediction. S8, Correcting the importance probability density function: Using the similarity metric from step S7 to guide the generation of a new proposal distribution, thereby updating the importance probability density function in step S6 to compensate for the correction of the Monte Carlo sampling process; S9, Update Markov Importance Weights: Update the importance weights of the first-order Markov model in step S6 using the proposed distribution corrected in step S8, and normalize the particle weights to obtain the prediction results of the welding forming state at the current moment. S10, steps S5-S9 constitute an iterative process for predicting and estimating the welding forming state using a particle filtering method based on state trajectory clustering similarity; repeat steps S6-S9 to sequentially output the prediction results of ship GMAW weld forming using clustering similarity particle filtering.

2. The method for predicting the formation of GMAW weld seams in ships based on particle filtering as described in claim 1, characterized in that, In step S31, the effects of interference noise on the prediction model of dynamic forming of hull structure welding are divided into two categories: deterministic interference and random interference noise. Deterministic measurement information... It can be represented as: In the formula, , , These represent the system's measured values, true values, and deterministic interference noise, respectively. Random measurement information It can be represented as: In the formula, random measurement information yes , Non-additivity function, It is random interference noise. Refers to the moment of data collection.

3. The method for predicting the formation of GMAW weld seams in ships based on particle filtering as described in claim 2, characterized in that, The time-domain expression of the nondeterministic noisy Hammerstein stochastic system model described in step S32 is as follows: in, for dimensional vector; for dimensional vector; The order of the linear subsystem; The highest power of the nonlinear element; This is the equivalent composite noise; These are the model structure and parameters, respectively.

4. The method for predicting the formation of GMAW weld seams in ships based on particle filtering as described in claim 1, characterized in that, Step S33 Includes the following steps: First, the pure delay coefficient is determined using the step response identification method; second, assuming the order of the linear subsystem, the highest power of the nonlinear element is obtained using the recursive least squares method; finally, the optimal selection and evaluation of the order of the linear subsystem is performed using the final prediction error criterion.

5. The method for predicting the formation of GMAW weld seams in ships based on particle filtering as described in claim 3, characterized in that, In step S35, the steps of optimizing and identifying the model structure of the stochastic model of the ship GMAW welding dynamic process using the least squares identification method and the final prediction error criterion include: after determining the pure delay coefficient of the welding process parameters, first assuming that the order of the linear subsystem is known, and then taking the time-domain expression of the nondeterministic noise Hammerstein stochastic system model. The least squares normal equation is obtained: Error criterion function: Taking the minimum value of the error criterion function, the least squares solution is obtained as follows: Model parameter correspondence The above algorithm slows down as the amount of data increases, and too much old information weakens the effect of new information. Considering the real-time nature of the model structure, a recursive least squares identification method is adopted, assuming that the measured... The least squares normal equation for a set of observation data is: When the first Group data At that time, assumed Then the recursive formula is The above formula can be simplified to The initial value for recursion can be selected as follows: The final error criterion of the recursive algorithm: in, .

6. The method for predicting the formation of GMAW weld seams in ships based on particle filtering as described in claim 1, characterized in that, The method for dividing the preprocessed welding information from step S2 into a training set and a test set in step S4 is as follows: Using the welding information preprocessed in step S2 as the original dataset, a Bayesian tracking training model is established to determine the parameters of the state equation: the first S sets of data from the preprocessed original historical dataset AX are used as the training set AT for state tracking training, i.e., AT=AX(1:S,:)=[ATI, ATV, …, ATB, ATD, …], where ATI, ATV, ATB, and ATD represent the tracking sets of welding current, wire fill rate, and corresponding weld width and penetration depth, respectively; the data TX after the S sets of the preprocessed original dataset AX are used as the test set for comparison between the true and predicted values, i.e., TX=AX(:,S+1:N)=[TXI,TXV, …, TXB, TXD, …]; using Bayesian theory, the test set AT is used for state tracking training modeling, and the optimal model parameters that minimize the error between the algorithm's predicted values ​​and the experimental true values ​​are estimated using minimum variance unbiased estimation, thereby improving the state space equation for welding formation prediction.

7. The method for predicting the formation of GMAW weld seams in ships based on particle filtering as described in claim 1, characterized in that, Step S7 includes: S71, Joint Trajectory Feature Mining and Vector Programming in State Space: Select from arrive The set of particles representing the joint trajectory of the welding forming state at any given time is ,in obey Filtering process, obey Prediction process, The length of the filtered trajectory. To predict the trajectory length, since the actual welding forming state of the system is unknown, the consistency of the forming state trajectory is characterized by the likelihood function of the process observation. The corresponding likelihood trajectory is solved by the process observation equation based on the forming state trajectory of the sampled particles. ,in: S72, Similarity Measurement of Actual Welding Formation State and Particle Process Observation Likelihood Trajectory: The method for measuring the similarity between the measurement information predicted by the current stage filtering and the future multi-stage Gaussian filtering using cluster analysis is as follows: The likelihood trajectory of the process observation corresponding to the actual welding system formation state is... Spatial trajectory clustering consistency analysis was employed, using distance similarity as a metric to measure the distance similarity between the actual welding forming state and the likelihood trajectory observed by the particle process. The calculation is as follows: in The distance similarity function is represented, and , For metric type parameters; To enhance the reliability of the algorithm's output, an exponential function structure is used to perform an exponential transformation on the above equation to obtain an updated similarity metric. in, This is the reliable gradient factor.

8. The method for predicting the formation of GMAW weld seams in ships based on particle filtering as described in claim 7, characterized in that, Step S8 includes: based on the distance similarity measure between the process observation likelihood trajectory and the measured likelihood trajectory of the sampled particles obtained in step S72, applying the following formula to correct the prior probability distribution using the similarity measure. The importance probability density function of substitution : 。

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